Wave filter



Patented Apr. 30. 1940 UNITED STATES WAVE FILTER George William Gilman,London, England, as

signor to Bell Telephone 'porated, New York, N. Y.,

New York Laboratories, Incora corporation 'of' Application August 20,193s, Serial No. 225,901 8 Claims. (01. 17844).

openr-circuited transmission lines coupled gelectro- This inventionrelates .to wave filters and more particularly to wave filters for highfrequencies in which the selective transmission properties are obtainedby the use of sections of uniform-transmission lines of low dissipation.

Heretofore it has been the practice in the construction of transmissionline wave filters to use open-circuited or short-circuited line sectionsas two-terminal impedance elements, appropriate elements being combinedin series-shunt or in other configurations in accordance with the kindof selective characteristic desired.

In the present invention, anovel configuration is employed according towhich open-circuited or short-circuited line sections areelectromagnetically coupled to each other along their lengths, wherebywave energy is transferred from the input terminals of one line to theoutput terminals of another with a band frequency selectivecharacteristic which is determined by the character and degree of thecoupling.

The lines may be open-wire types or they may be of the shieldedconductor type and the coupling is preferably effected by running theconductors parallel to each other along their length. The degree ofcoupling may be modified by the interposition of partial electrostaticscreens between the conductors or by proportioning their dimensions andseparations.

The. filters of the invention are characterized by multiple pass-bandsspaced at harmonic frequency intervals. The width of the bands and theamount .of attenuation in the intervening frequency ranges is controlledby the degree of coupling between the lines.

Otherfeatures of the invention and the principles'underlying itsoperation will be more fully understood from the following detaileddescrip tion and by reference to the attached drawing, of which Figs. 1and 1a are schematic diagramsillustrating one general form of theinvention;

Fig. 2 shows an alternative general form of the invention;

Figs. 3 and 4 are schematic diagrams illustrating tandem arrangements ofthe forms shown in Figs. 1 and 2, respectively; and

Figs. 5, 6 and '7' are illustrative of mechanical constructions used inmodifications of the invention. e I I Referring to Figs.,1 and 1a,elements I and 2 represent two I elevated conductors; of equal lengthslying parallel to each other at a height 71. above ground and separatedby a distance d. Between one end of-linel and ground is connected a highfrequency generator 3 and a load resistance 4 is connected from theremote end of line 2 to ground. Conductors l and 2 and the commonground; return constitute a pair of magnetically to each other alongtheir lengths by virtue of their juxtaposition. Transmission takes placein the system from the generator 3 to the load through the distributedcoupling and, because of the character of the coupling and the currentand voltage distributions in the two lines. exhibits a definite bandselective characteristic. The center of the first transmission band liesat the frequency for which the lengths of'the two conductors are equalto a quarter of the propagation wave-length, that is, for which theconductors become quarter wave lines. The other transmission bands arelocated at certain equally spaced harmonic frequencies above the firstband.

The manner in which the transmission bands are formed andthe dependenceof the selective characteristics uponthe line parameters is explained bythe followingmathematical analysis.

It will be assumed that the effects of resistance in the two' conductorsand the return path are negligibly small so that the wave propagationvelocity in the system may be taken as equal to the velocity of light.Fields other than radial fields may be disregarded and the steadydistribution of oscillatory currents in the lines may be represented bythe equations and v 1 wherein I1(x) and I2(x) are the currents inconductors I and 2 respectively at points distant (at) from thegenerator, the As and the Bs are factors determined by the terminal orboundary conditions and the impressed voltage, and 'y is the propagationconstant of the individual lines.

The quantity '7' is a pure imaginary in the absence of resistance andhas the value where w is 2-- times frequency and'b is the veloo- I point:0, Q1 and Qz,-the charges per unit length on lines I. and 2respectively at the given point, and p11, p12, and .1122. are theMaxwell potential coefl lcientsof the system.- 1

.55 where V101) and V2(x) represent the voltages at By means of thegeneral steady state relationship and (5) When the two conductors aresimilar and the system is symmetrical, the coefficients p11 and 1 22 areequal. Hereinafter, symmetrical systems will be assumed and thenotations p and 1 m will be used in place of p11, p22 and. p12,respectively.

Since the system is symmetrical longitudinally, its general imageparameters can be determined by solving Equations 1 and for theparticular case in which the load terminals are short-circuited. Theestablishment of the boundary con ditions corresponding to this casepermits the determination of the appropriate values of the As and the Bsand thereafter of the shortcircuit input impedance at the generator endand the short-circuit transfer impedance from the source to the outputterminals. These latter quantities suflice for the computation of theimage impedance and the image transfer constant of the symmetricalsystem.

The boundary conditions when the load terminals are short-circuited areV =E and 1 0 when x=0 and V =O and I1='0 when=s S denoting the wholelength of the lines and E the terminal voltage of generator 3. Theapplication of these boundary conditions to Equations 1 and 5 gives anew set of equations, namely,

These equations can be solved for the As and Bs, the values of which arefound to be The determination of the significant parameters of thecomplete system, namely, the image transfer constant and' the imageimpedance'requires only the knowledge of two impedances, namely,

the input impedance at the generator end when the output of line 2 isshorted and the transfer impedance from the generator to the short-circuited output of line 2. Denoting the input end impedance by Z0 and thetransfer impedance by ZT, their values are found from Equations with thehelp of Equations 7 to 10, to be 41s (11) p1) sin and 2 ie 1 Z 2' J p n229 1) s1 7 X wherein I) .21r f 'Y I being the frequency, and denotesthe wavelength of the current in the line.

The image impedance K, which is the same for both ends of the system, isgiven by The transmission bands are located in the ranges for which K-isreal and tanh 0 imaginary and the band limits are determined'as thefrequencies at which thesequantities change from reals to imaginaries.From the character of Equations 14 and 16 it is evident that, the bandlimits are defined by the relationship p 21i-S E 008 T :l: 1

The potential coefficients :0 and 20m are of the nature of inversecapacities and are related to the capacities of the system as follows.As shown in Fig. la, the system of conductors'has three significantcapacities, namely, the direct mutual capacity between conductors l' and2, which is designated Cm, and the direct capacities of each wire toground, which in the example illustrated are equal and are designated C.These capacities are the capacities per unit length of the line. Thevalues of the potential coefi'icients in terms of the capacitiesare'gi'ven by The lowest frequency band has its center at the frequencyfor which 7,

A 1 that is, for which the conductors are quarter wave-length lines. Theother bands are centered at the odd harmonics of this frequency. Thecut-oif frequencies in terms of the line capacities are given by 27FS mcos -cos ic+cm from which it is evident that the smaller Cm is withrespect to C, the narrower will be the resulting band. A band width ofabout ten per cent of the mid-band frequency is obtained byproportioning the size and spacing of the conductors so that Cm is aboutone-twelfth of C.

The image impedance is zero at the band edges and rises to the value Km,given by at the center of the band. Absolute or c. g. s. units areassumed in all of the preceding formulae, the value of 11 being 3x10centimeters per second. The capacities C and Cm are the capacities percentimeter length of the conductors. If these capacities are measured inmicromicrofarads per centimeter, Equation 21 becomes The modified filtercircuit shown in Fig. 2 corresponds to that of Fig. 1 except that thefree ends of the two conductors are short-circuited instead of beingopen-circuited. In both types the free ends of the conductors'areterminated to provide full wave reflection. The transfer constant of thefilter of Fig. 2 is the same as that of Fig. 1 and has the value givenby Equation 16. The image impedance is the reciprocal of the expressionin Equation 14 except for a constant multiplier. Its value becomesinfinite at the edges of the transmission band and at the mid-bandfrequency drops to a minimum which is inversely proportional to thecoupling as measured by pm or Cm.

The open-circuit type shown in Fig. 1 has an ohms (22) impedancecharacteristic of the form exhibited by mid-series terminated filtersand is characterized by a relatively low impedance in the transmissionbands. The modified form shown in Fig. 2 resembles amid-shunt'terminated filter and is characterized by a relatively highimage impedance in the transmission bands.

Since the filters are symmetrical longitudinally, similar sections maybe connected in tandem to provide increased discrimination. The tandemconnection of two sections of the type shown in Fig. 1 is illustrated inFig. 3. The resulting structure comprises two quarter wave open-circuitwave conductors 5 and I paralleled by a half wave-length open-circuitconductor 6. A corresponding arrangement of two sections of theshort-circuited type is shown in Fig. 4. Manifestly, additional sectionsmay be added in any desired number.

Instead of using open wires with a common ground return, the filters ofthe invention may comprise a pair of conductors symmetrically disposedwithin a surrounding tubular conductor which constitutes the commonreturn path. A cross-section of a line of this type is shown in theshield. For this purpose, it is desirable to separate the conductors aswidely as practicable and to keep their diameters small. The reductionof the direct capacity may, however, be secured more advantageously bythe use of a partial shield interposed between the conductors, as shownin Fig. 6.

In Fig. 6 the outer shellis composed of two fianged channel sections 9and Ill which are welded or soldered toa perforated copper screeningplate ll coextensive in length with the conductors. Plate II is solidexcept for a series of perforations such as shown at l2 in Fig. 7extending along its axis. These perforations should be close togetherand uniform in size to maintain a substantially continuous longitudinaldistribution of the mutual capacity. The size of the apertures may bedetermined experimentally to provide a desired relationship between themutual capacity Cm and the shield or ground capacities C.

What is claimed is:

1. A band selective transmission system comprising a pair of similartransmission lines disposed parallel to each other and electrostaticallycoupled, a wave source connected to one end of one of said lines, and aload impedance connected to the remote end of the other of said lines,both of said lines being terminated at their free ends to produce fullwave reflection and the lengths of the lines being equal to onequarparallel thereto and disposed symmetrically with respect to saidconductors, terminal means for connecting a wave source between one endof one of said conductors and said common return, and terminal means forconnecting a load impedance between the remote end of the other of saidconductors and said common return, said conductors being terminated attheir free ends for full-wave reflection, and their lengths being equalto quarter wave-lengths at an assigned frequency whereby the system hasa finite transmission band centered about said assigned frequency.

5. A wave filter in accordance with claim 4 in which the direct mutualcapacity between said conductors is small in comparison with'thecapacity of each conductor to the return path, whereby a narrowtransmission band is provided.

6. A wave filter in accordance with claim 4 in u capacity is made smallwith respect to their 'direct capacities to the shield.

8. A system in accordance with claim 1 including a partial electrostaticshield interposed between the said lines.

GEORGE WILLIAM GILMAN.

